If your game is the same as the English version I have then this is what you do to have more than 1 family:
1. Open your game as you usually do, then click the Menu button at the lower-left of the game screen.
2. Click in the box right below where it says Current Player. It will take you to a list of 5 game slots. The first slot is for the first family you started.
3. Click the second slot and type in a name for your new family (I can't test this part to make sure because I already have 5 games).
4. Click "OK" and then you should be good to go.
5. To switch between families you have to follow Steps 1 and 2 again and choose the game you want to open. It will automatically open to whichever family was last played.